Research

The age of data and network-based sciences has definitely arrived. The largescale generation of data such as financial, chemical, technical and social data sets allows the construction of complex networks that often provide a new framework for understanding relations complex relationships and dynamics. My research activities relate to thoroughly investigate data driven network-based techniques for exploring properties of complex networks. This involves using algorithms from Graph Theory, Information Theory, Statistics and Data Analysis. I have published extensively in Applied Mathematics, Data Science, Machine Learning and related disciplines.

My research can be roughly divided into the following categories:

Graph Theory and Complex Networks

Graphs are currently ubiquitous in many disciplines. Roughly, graph theory can be divided into descriptive and quantitative graph theory. However, quantitative techniques, such as measures which capture structural information of graphs, turned out to be important. Quantitative Graph Theory was mainly developed by Dehmer and Emmert-Streib, see [1,2]. Important problems in quantitative graph theory are graph similarity [2,7], graph complexity [1,3,4], and investigating properties of structural network measures [5,6,8].

Subset of related work:

  1. Dehmer M., Emmert-Streib F.: Quantitative Graph Theory: Mathematical Foundations and Applications, CRC Press, 2014
  2. Dehmer M., Emmert-Streib F., Shi Y.: Quantitative Graph Theory: A new branch of graph theory and network science, Information Sciences, Vol. 418-419C, 2017, 575-580
  3. Liu W., Ban J., Feng F., Cheng T., Emmert-Streib F., Dehmer M.: The Maximum Hosoya Index of Unicyclic Graphs with Diameter at Most Four, Symmetry Vol. 11 (8), 2019, 1034
  4. Ghorbani M., Hakimi-Nezhaad M., Dehmer M., Li X.: Analysis of the Graovac-Pisanski Index of Some Polyhedral Graphs Based on Their Symmetry Group, Symmetry, Vol. 12 (9), 2020
  5. Ghorbani M., Rajabi-Parsa M., Dehmer M., Mowshowitz A., EmmertStreib F.: On Properties of Distance-based Entropies on Fullerene Graphs, Entropy, Vol. 21 (482), 2019
  6. Wan P., Chen X., Tu J., Dehmer M., Zhang S., Emmert-Streib F.: On graph entropy measures based on the number of independent sets and matchings, Information Sciences Vol. 516, 491-504, 2020
  7. Dehmer M., Chen Z., Shi Y., Zhang Y., Tripathi S., Ghorbani M., Mowshowitz A., Emmert-Streib F.: On efficient network similarity measures, Applied Mathematics and Computation, Vol. 362, 2019, 124521
  8. Mowshowitz A., Dehmer M.: Entropy and the Complexity of Graphs Revisited, Entropy, Vol. 14 (3), 2012, 559-570
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Symmetry in Graphs

Various graph-theoretical measures have been developed over the years to quantify structural features of networks. Symmetry in graphs as a type of structural complexity and automorphisms [1,4] have been among the most important graph properties in various disciplines. Investigating symmetry relates to determine and study the automorphism group of a graph. I have been examining this problem extensively, in particular I put the emphasis on exploring polynomial-based symmetry measures [2,3] for graphs.

Subset of related work:

  1. Ghorbani M., Dehmer M., Lotfi A., Amraei N., Mowshowitz A., EmmertStreib F.: On the relationship between PageRank and automorphisms of a graph, Information Sciences, Vol. 579, 401-417, 2021
  2. Ghorbani M., Alidehi-Ravandi R., Dehmer M., Emmert-Streib F.: A Study of Roots of a Certain Class of Counting Polynomials, Mathematics, Vol. 11 (13), 2876, 2023
  3. Lotfi A., Mowshowitz A., Dehmer M., A Note on Eigenvalues and Asymmetric Graphs, Axioms, Vol. 12 (6), 510, 2023
  4. Varmuza K., Dehmer M., Emmert-Streib M., Filzmoser P.: Automorphism Groups of Alkane Graphs, Croatica Chemica Acta, Vol. 94 (1), 47-58
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Information Theory of Networks

My focus in this area has been to develop novel entropy measures [2,3,4] for graphs which characterize the topology of structural data sets, e.g., networks and graphs. The research in this area started in the fifties and poses challenging problems since decades. I devloped the partition-independet graph entropy measures [5,6,7] based on information functionals. Besides developing graph entropy measures extensively, I have been investigating extremal properties [1] of graph entropy measures and other structural graph measures.

Subset of related work:

  1. Kraus V., Dehmer M., Schutte M.: On Sphere-Regular Graphs and the Extremality of Information-Theoretic Network Measures, MATCH Commun. Math. Comput. Chem., Vol. 70 (3), 2013, 885-900
  2. Dehmer M., Mowshowitz A.: Generalized Graph Entropies, Complexity, Vol. 17 (2), 2011, 45-50
  3. Dehmer M., Mowshowitz A., Emmert-Streib F.: Connections between Classical and Parametric Network Entropies, PLoS ONE, Vol. 6 (1), 2011, e15733
  4. Dehmer M., Mowshowitz A.: A History of Graph Entropy Measures, Information Sciences, Vol. 1 (1), 2011, 57-78
  5. Emmert-Streib F., Dehmer M.: Networks for Systems Biology: Conceptual Connection of Data and Function, IET Systems Biology, Vol. 5 (3), 2011, 185-207
  6. Dehmer M., Emmert-Streib F: Structural Information Content of Networks: Graph Entropy based on Local Vertex Functionals, Computational Biology and Chemistry, Vol. 32, 2008, 131-138
  7. Dehmer M., Emmert-Streib F: The Structural Information Content of Chemical Networks, Zeitschrift für Naturforschung A, Vol. 63a, 2008, 155-158
  8. Dehmer M., Borgert S., Emmert-Streib F.: Entropy Bounds for Hierarchical Molecular Networks, PLoS ONE, Vol. 3 (8), 2008, e3079
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Data Science

In the context of Data Science and Machine Learning, I have been active towards designing data analysis methods to analyze data from the web, computational finance and bioinformatics, see [1,2,3]. This also involves the application of text mining techniques [4,5] as well as the study of related fields such as Information Fusion [6].

Subset of related work:

  1. Emmert-Streib F., Tripathi S., Dehmer M.: Human team behavior and predictability in the massively multiplayer online game WOT Blitz, ACM Transactions on the Web, Vol. 18 (1), 2023, 1-27
  2. Emmert-Streib F., Tripathi S., Dehmer M.: Analyzing the scholarly literature of digital twin research: Trends, topics and structure, IEEE Access, Vol. 11, 2023
  3. Emmert-Streib M., Dehmer M.: Taxonomy of machine learning paradigms: A data-centric perspective, Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery Vol. 12 (5), 2022
  4. Perera N., Nguyen TTL., Dehmer M., Emmert-Streib F.: Comparison of text mining models for food and dietary constituent named-entity recognition, Machine Learning and Knowledge Extraction, Vol. 4 (1), 2022, 254-275
  5. Bashath S., Perera N., Tripathi S., Manjang K., Dehmer M., EmmertStreib.: A data-centric review of deep transfer learning with applications to text data, Information Sciences, Vol. 585, 498-528, 2022
  6. Holzinger A., Dehmer M., Emmert-Streib F., Cucchiara R., Augenstein I., Del Ser J., Samek W., Jurisica I., Diaz-Rodriguez N.: Information fusion as an integrative cross-cutting enabler to achieve robust, explainable, and trustworthy medical artificial intelligence, Information Fusion, Vol. 79, 263-278, 2022

Prof. Dr. habil. Matthias Dehmer

UMIT – The Health and Lifesciences University, Eduard Wallnoefer Zentrum 1, A-6060 Hall in Tyrol, Austria Swiss Distance University of Applied Sciences, Department of Computer Science, Brig, Switzerland, Nankai University, China, College of Artificial Intelligence, Tianjin, China.

matthias.dehmer@ffhs.ch

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